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Trudy Mat. Inst. Steklova, 2017, Volume 296, Pages 72–94 (Mi tm3766)  

This article is cited in 4 scientific papers (total in 4 papers)

On the zeros of the Davenport–Heilbronn function

S. A. Gritsenkoab

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Bauman Moscow State Technical University

Abstract: Let $N_0(T)$ be the number of zeros of the Davenport–Heilbronn function in the interval $[1/2,1/2+iT]$. It is proved that $N_0(T)\gg T(\ln T)^{1/2+1/16-\varepsilon }$, where $\varepsilon $ is an arbitrarily small positive number.

DOI: https://doi.org/10.1134/S037196851701006X

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 296, 65–87

Bibliographic databases:

UDC: 511.331
Received: May 15, 2016

Citation: S. A. Gritsenko, “On the zeros of the Davenport–Heilbronn function”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 72–94; Proc. Steklov Inst. Math., 296 (2017), 65–87

Citation in format AMSBIB
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\paper On the zeros of the Davenport--Heilbronn function
\inbook Analytic and combinatorial number theory
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov
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\vol 296
\pages 72--94
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    This publication is cited in the following articles:
    1. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. S. A. Gritsenko, “O drobnykh momentakh uspokoennykh $L$-funktsii Lirikhle”, Chebyshevskii sb., 18:4 (2017), 168–187  mathnet  crossref
    3. Z. Kh. Rakhmonov, Sh. A. Khairulloev, A. S. Aminov, “Nuli funktsii Devenporta–Kheilbronna v korotkikh promezhutkakh kriticheskoi pryamoi”, Chebyshevskii sb., 20:4 (2019), 306–329  mathnet  crossref
    4. M. K. Das, S. Pujahari, “Distribution of signs of karatsuba's and generalized davenport-heilbronn z-functions”, J. Number Theory, 212 (2020), 409–447  crossref  mathscinet  zmath  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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